Circle packing coordinates for the moduli space of tori

Williams, G.

doi:10.1090/S0002-9939-2010-10690-1

Circle packing coordinates for the moduli space of tori

Author: G. Brock Williams
Journal: Proc. Amer. Math. Soc. 139 (2011), 2577-2585
MSC (2010): Primary 52C26, 30F60
DOI: https://doi.org/10.1090/S0002-9939-2010-10690-1
Published electronically: December 17, 2010
MathSciNet review: 2784827
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Abstract: We develop a set of natural coordinates $(\alpha,\beta)$ on the moduli space of Euclidean tori using the combinatorial structure of circle packings. Surfaces with rational coordinates support Brooks packings, while surfaces with rational $\alpha$ and irrational $\beta$ coordinates support generalized Brooks packings with periodic singularities.

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